In mathematics, a locally constant function is a function from a topological space into a set with the property that around every point of its domain...

called the Lipschitz constant of the function (and is related to the modulus of uniform continuity). For instance, every function that is defined on an...

In mathematics, a constant function is a function whose (output) value is the same for every input value. As a real-valued function of a real-valued argument...

still be locally finite, resulting in the definition of piecewise constant functions. A constant function is a trivial example of a step function. Then there...

a bounded function, for which the constant does not depend on x . {\displaystyle x.} Obviously, if a function is bounded then it is locally bounded. The...

In mathematics, a locally integrable function (sometimes also called locally summable function) is a function which is integrable (so its integral is...

constant of integration, often denoted by C {\displaystyle C} (or c {\displaystyle c} ), is a constant term added to an antiderivative of a function f...

In algebraic topology, a locally constant sheaf on a topological space X is a sheaf F {\displaystyle {\mathcal {F}}} on X such that for each x in X, there...

functions will yield another harmonic function. Finally, examples of harmonic functions of n variables are: The constant, linear and affine functions...

is a locally constant function on X. In particular, if X is connected (that is if R has no other idempotents than 0 and 1), then P has constant rank....

can be expressed as the ratio between two holomorphic functions (with the denominator not constant 0) defined on D: any pole must coincide with a zero of...

This sheaf may be identified with the sheaf of locally constant A {\displaystyle A} -valued functions on X {\displaystyle X} . In certain cases, the set...

general form of the antiderivative replaces the constant of integration with a locally constant function. However, it is conventional to omit this from...

function f, exp(f) is a non-vanishing holomorphic function, and exp(f + g) = exp(f)exp(g). Its kernel is the sheaf 2πiZ of locally constant functions...

monotone are not invertible because they are constant on some interval (and therefore are not one-to-one). A function may be strictly monotonic over a limited...

construction quotient Topological tensor product Discrete space Locally constant function Trivial topology Cofinite topology Cocountable topology Finer...

complex-valued function f on d-dimensional Euclidean space satisfies a Hölder condition, or is Hölder continuous, when there are real constants C ≥ 0, α >...

mathematics, a Schwartz–Bruhat function, named after Laurent Schwartz and François Bruhat, is a complex valued function on a locally compact abelian group, such...

the Lie bracket of vector fields, but this is true only up to a locally constant function. However, to prove the Jacobi identity for the Poisson bracket...

that a holomorphic function is infinitely differentiable and locally equal to its own Taylor series (is analytic). Holomorphic functions are the central...

( G ) {\displaystyle C_{c}^{\infty }(G)} denote the space of locally constant functions on G {\displaystyle G} with compact support. With the multiplicative...

group A {\displaystyle A} , the constant sheaf A X {\displaystyle A_{X}} means the sheaf of locally constant functions with values in A {\displaystyle...

functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector...

analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions...

is a locally free OS-module of finite rank. The rank is a locally constant function on S, and is called the order of G. The order of a constant group...

is a differentiable function between manifolds, the inverse function theorem gives conditions for this to be single-valued locally in X. For example, the...

be called "exact". The cohomology classes are identified with locally constant functions. Using contracting homotopies similar to the one used in the proof...

Sawtooth function Floor function Step function, a function composed of constant sub-functions, so also called a piecewise constant function Boxcar function, Heaviside...

In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional...

In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups,...